Abstract High dimensional robot motion planning has recently been approached with trajectory optimization methods that efficiently minimize a suitable objective function in order to generate robot trajectories that are both optimal and feasible. However, finding a globally optimal solution is often an insurmountable problem in practice and state-of-the-art trajectory optimization methods are thus prone to local minima, mainly in cluttered environments. In this paper, we propose a novel trajectory planning algorithm that employs stochastic optimization in order to find a collision-free trajectory generated from a continuous-time Gaussian process (GP). The contributions of the proposed motion planning method stem from introducing the heteroscedasticity of the GP, together with exploited sparsity for efficient covariance estimation, and a cross-entropy based stochastic optimization for importance sampling based trajectory optimization. We evaluate the proposed method on three simulated scenarios: a maze benchmark, a 7 DOF robot arm planning benchmark and a 10 DOF mobile manipulator trajectory planning example and compare it to a state-of-the-art GP trajectory optimization method, namely the Gaussian process motion planner 2 algorithm (GPMP2). Our results demonstrate the following: (i) the proposed method yields a more thorough exploration of the solution space in complex environments than GPMP2, while having comparable execution time, (ii) the introduced heteroscedasticity generates GP priors better suited for collision avoidance and (iii) the proposed method has the ability to efficiently tackle high-dimensional trajectory planning problems.

中文翻译：

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使用异方差连续时间高斯过程的基于交叉熵的机器人轨迹随机优化

摘要 高维机器人运动规划最近采用轨迹优化方法进行处理，该方法有效地最小化合适的目标函数，以生成既最优又可行的机器人轨迹。然而，寻找全局最优解在实践中往往是一个无法解决的问题，因此最先进的轨迹优化方法容易出现局部最小值，主要是在杂乱的环境中。在本文中，我们提出了一种新颖的轨迹规划算法，该算法采用随机优化来寻找由连续时间高斯过程 (GP) 生成的无碰撞轨迹。所提出的运动规划方法的贡献源于引入 GP 的异方差性，以及用于有效协方差估计的稀疏性，以及基于交叉熵的随机优化，用于基于重要性采样的轨迹优化。我们在三个模拟场景中评估了所提出的方法：迷宫基准、7 DOF 机器人手臂规划基准和 10 DOF 移动机械手轨迹规划示例，并将其与最先进的 GP 轨迹优化方法（即高斯）进行比较过程运动规划器 2 算法 (GPMP2)。我们的结果证明了以下几点：(i) 与 GPMP2 相比，所提出的方法在复杂环境中对解空间进行了更彻底的探索，同时具有可比的执行时间，(ii) 引入的异方差性生成了更适合避免碰撞的 GP 先验，以及 (iii) ) 所提出的方法能够有效地解决高维轨迹规划问题。